Question

1. Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 2.1. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2005?

   ______________________people

(Note: once diseases become widespread, they start to behave more like logistic growth, but don't worry about that for the purpose of this exercise)

2 . A population grows according to an exponential growth model. The initial population is P0=10, and the growth rate is r=0.45.

Then:

P1 =

P2 =

Find an explicit formula for Pn. Your formula should involve n.

Pn =   

Use your formula to find P12

P12 =

Give all answers accurate to at least one decimal place

3 . Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1800 fish. Absent constraints, the population would grow by 240% per year.

If the starting population is given by p0=500, then after one breeding season the population of the pond is given by

p1 =   

After two breeding seasons the population of the pond is given by

p2 =   

Answer 1

Drop a comment if u have any doubt. Upvote if u like it.

Thank you.